On a generalized resolvent estimate for the Stokes system with Robin boundary condition
Yoshihiro Shibata, Rieko Shimada · Journal of the Mathematical Society of Japan · 2007
We prove a generalized resolvent estimate of Stokes equations with nonhomogeneous Robin boundary condition and divergence condition in the L q framework ( 1 ν = h on the boundary of the domain with α , β ≥ 0 and α + β = 1 , where u denotes a velocity vector, p a pressure, T ( u , p ) the stress tensor for the Stokes flow, and ν the unit outer normal to the boundary of the domain. It presents the slip condition when β = 1 and the non-slip one when α = 1 , respectively.